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This could be a historic moment in the Treasury market

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All of a sudden, the talk about the U.S. 10-year yield heading to World War II lows does not sound all that far-fetched.

That yield stands tall compared to the yields of the sovereigns from other developed nations.

The 10-year Japanese government bond, for instance, has a negative yield, and yield edged down to 0.08 percent Tuesday, closing in on its April 2015 intraday low of 0.04 percent.

Analysts say the driver for U.S. long-end yields right now is the interest rate differential between the U.S. and these other sovereigns. The U.S. yield is attractive when looking at a basket of global bonds.

John Kosar, chief strategist at Asbury Research, says he expects to see another 3 to 5 percent move higher in long-dated Treasury prices. That would put his next target for the 10-year yield at 1.70 percent. Yields move inversely to prices.

The 10-year was yielding 1.71 Tuesday afternoon. The low close for 2016 was 1.63 percent in February, and traders are also watching that level.

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Kosar, a technician, also looks at monthly charts, so after 1.70, he is watching the 1.55 to 1.51 percent area, as a second potential target. That was a key monthly closing level from 2012, and also all the way back to 1945.

Below that, he would be watching 1.43 percent, a daily closing low from July 2012.

"We were right there in July 2012. We have two major lows that have been made in yields. One was in the 1940s, and one was in 2012," said Kosar.

The low yield in July 2012 on an intraday basis was a stomach-knotting 1.38 percent, according to Thomson Reuters charts.

Analysts say that a catalyst is needed to send yields spiraling that low and it could come from outside of the United States.

As for the 10-year yield falling to 1.43 percent, "I wouldn't rule it out," said Jim Caron, fixed income portfolio manager at Morgan Stanley Investment Management. "I would not balk at that number. It really is highly dependent on a lot of facts. What goes on with the Saudi oil deal ... does oil return to the sub-$30 level?"

He said the market is focused on whether Saudi Arabia agrees with other producers at an April 17 meeting to freeze output, now that oil prices have fallen back into the mid-$30s.

Caron said all it might take to push the 10-year yield to those lows is "the absence of decent news. If oil leaks back down to $30 or China does something really abrupt in terms of their currency setting or we move into 'Brexit' risk with the U.K."

He said the market is being driven by risk premia. "There's all types of things that go into that. ... There are two things that are driving risk premium in the market, one is China and one is oil prices," he said.

Caron said U.S. GDP, now tracking at a half percent for the first quarter, is a factor in the 10-year yield but it's more driven by external issues.

"It's obviously dependent on what's going on in the world. The thing with the 10 year is there's not a lot of U.S. economic influence on it. The 10 year has become very globalized in terms of its performance. Whatever is going on in the world, the 10 year is going to reflect. The two year might reflect what's going on with the Fed and things like that."

Caron said on the high side, the 10-year yield could see between 2.15 and 2.25 percent.

"Yields tend to revisit old inflection points," said Kosar.

"We're looking for a move down to 1.70 and from there we'll see what things look like. We think it has the potential to go to 1.43 but one step at a time," he said.